An adjusting device of this kind having an actuator that is provided with two mutually engaging gear wheels having helical toothing, is known from the German Patent Application DE 44 08 425 A1. One of the gear wheels is coupled to the camshaft, and the other is driven via a chain by the crankshaft. The gear wheels can be axially shifted towards one another by a hydraulic mechanism, thereby producing a relative torsion between the crankshaft and camshaft due to the helical toothing. The hydraulic mechanism is driven by an actuating signal generated by a control circuit. The hydraulic mechanism is controllable in each instance by one of three values, namely by an early value for adjusting the camshaft toward an early opening of the intake valves of the combustion engine, by a late value for adjusting the camshaft toward a late opening of the intake valves, and by a hold value for holding the active actual angular position. The control circuit executes a control program, which, for each program run, estimates the adjustment speed that will exist at the beginning of the following program run. From this estimated value and the known time response of the camshaft adjustment following the switching of the hold value over to the actuating signal (early or late value), the adjustment angle that the angular position of the camshaft would still change to, if the actuating signal were changed over to the hold value at the beginning of the next program run, is estimated. When the deviation between the estimated value for the adjustment angle and the setpoint angular position of the camshaft lies within a range of tolerance, the switch is made from the early or late value to the hold value. The adjustment speed that will presumably exist at the beginning of the following program run, is estimated from the current adjustment speed, using a first-order transfer function and a final adjustment speed. The final adjustment speed is adapted under specific conditions. In this way, according to the patent application, estimated values for the current position can be determined very precisely even when operating parameters of the hydraulic mechanism change, such as the viscosity of the hydraulic fluid, due to heating of the same. Nevertheless, the control accuracy of the control circuit is still in need of improvement, above all in different operating states. Thus, for example, an overshooting of the signal to be controlled can occur in certain operating situations.